next | previous | forward | backward | up | top | index | toc | Macaulay2 website
MultiprojectiveVarieties :: MultirationalMap | MultiprojectiveVariety

MultirationalMap | MultiprojectiveVariety -- restriction of a multi-rational map

Synopsis

Description

i1 : ZZ/33331[x_0..x_3], f = rationalMap {x_2^2-x_1*x_3,x_1*x_2-x_0*x_3,x_1^2-x_0*x_2}, g = rationalMap {x_2^2-x_1*x_3,x_1*x_2-x_0*x_3};
i2 : Phi = last graph rationalMap {f,g};

o2 : MultirationalMap (rational map from threefold in PP^3 x PP^2 x PP^1 to PP^2 x PP^1)
i3 : Z = (source Phi) * projectiveVariety ideal random({1,1,2},ring ambient source Phi);

o3 : ProjectiveVariety, surface in PP^3 x PP^2 x PP^1
i4 : Phi' = Phi|Z;

o4 : MultirationalMap (rational map from Z to PP^2 x PP^1)
i5 : source Phi'

o5 = Z

o5 : ProjectiveVariety, surface in PP^3 x PP^2 x PP^1
i6 : assert(image Phi' == Phi Z)

The following is a shortcut to take restrictions on random hypersurfaces as above.

i7 : Phi|{1,1,2};

o7 : MultirationalMap (rational map from surface in PP^3 x PP^2 x PP^1 to PP^2 x PP^1)

See also